polynomial (1 Viewer)

nfreidman · Sep 20, 2012

if p(x)=x^3-3x^2-9x+c has a double zero, find c.

SpiralFlex · Sep 20, 2012

$p(x)=x^3-3x^2-9x+c$

$p'(x)=3x^2-6x-9$

$For double zeros,$

$p(x)=p'(x)=0$

$3x^2-6x-9=0$

$(x-3)(x+1)=0$

$\therefore x=3,-1$

$$Case 1:$\; x = 3, p(3)=0, \therefore (3)^3-3(3)^2-9(3)+c=0$

$c=27$

$$Case 2:$\; x = -1, p(-1)=0, \therefore (-1)^3-3(-1)^2-9(-1)+c=0$

$c=-5$

polynomial (1 Viewer)

nfreidman

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SpiralFlex

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